Data measured with errors occur frequently in many scientific fields. In many real applications, the distribution of measurement error could vary with each subject or even with each observation so the errors are heteroscedastic. Estimating the probability density function from contaminated data with heteroscedastic errors could be achieved through the deconvolution kernel estimation method, where Fourier inversion and the kernel smoothing technique are applied to obtain the estimate. However, the convergence rates of the deconvolution kernel estimators could be very slow, and thus they may perform poorly in practice. In this talk, two new estimation methods are proposed: a simulation extrapolation (SIMEX)-type estimation method; and another nonparametric procedure named as Shannon Weighted Average Procedure (SWAP). The resulting estimators are stable and easy to compute -- there are no Fourier transformations needed in the calculation. The estimators have faster convergence rates than those of Fourier type estimators. The practical aspects of the proposed methods are illustrated through a newly developed open-source R package.

Key words : Deconvolution, density estimation, heteroscedastic measurement errors, Fourier inversion, simulation extrapolation (SIMEX), kernel methods.